 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2018/paper-1/section-c/c11/b/solution

Take a transverse offset

b \cdot R = 0

. Its distance from the source changes only at second order, but the direction of the gravitational force changes at first order:

g (R + b) = - \frac{GM}{R ^{3}} (R + b) + O (GM b^{2} / R^{4})

in its first-order vector expansion. Subtracting the reference acceleration gives

T (b) ≃ - \frac{GM}{R ^{3}} b .

It compresses the transverse separation. Together with the radial result, this is point-mass tidal stretching and squeezing, with tensor eigenvalues

(2, - 1, - 1) GM / R^{3}

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